X-Rays and xrf

8/4/2019 X-Rays and xrf

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X-rays and XRF

Physical aspects

P. Van Espen

Dept. of ChemistryUniversity of Antwerp, Belgium

[email protected]


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X-ray are part of the electromagnetic spectrum between ultraviolet radiationand gamma-rays.

The Nature of X-rays

When dealing with diffraction we best consider X-rays aselectromagnetic waves with wavelength

When discussing absorption and scattering X-rays are best considered asphotons with a certain energyE.

h Planck's constant (6.6254x10-34 J s)c the velocity light the wave (3.00x108 m/s) wavelength in meters

E Energy in joules.

Relation between energy and wavelength:

hc=E


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In X-ray spectrometry:

Wavelength in ngstrom units (1 = 0.1 nm = 10-10 m)

Energy in kilo-electronvolt (keV) 1 J = 6.24x1015 keV

Soft x-raysUltrasoft x-rays Hard x-raysUV ( -rays

100 10. 1.0 0.1Wavelength, 8

0.1 1.0 10. 100Energy, E keV

Analytical Range

U K"Be K" Fe K"

][

4.12[keV]

=E

Fe K E= 6.40 keV = 1.94

Be K E= 0.11 keV = 113

U K E= 98.4 keV = 0.126


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Interaction of X-rays with matter

The Bohr approximation of the atom

Z electrons are grouped in shells designated K, L, M, N, O, P

(principal quantum numbern = 1, 2, 3, 4, 5, and 6). A shell can have at maximum 2n2 electrons.

In each shell the electrons are further distinguished by their

azimuthal (l= 0, ... , n-1), magnetic (m = -l, ..., 0, ..., l) and spin (s = - , + )

quantum numbers. Two electrons in an atom cannot have the same set of quantum numbers(Pauli's exclusion principle).

The electrons in an atom occupy discrete energy levels.

K-shell electrons are more tightly bound than the L-shell electrons.

The number of energy levels (or sub-shells) in each shell is equal tothe number of allowed values of j (spin-orbit coupling), j = |l |.

The K-shell has 1 energy level, the L-shell has 3 (L1, L2, L3)and the M-shell has 5


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Shell n l= 0,...,n-1 j = |l | Max. number of electrons

2j+1

K 1 0 1/2 2

L1

L2

L3

2

2

2

0

1

1

1/2

1/2

3/2

2

2

4

M1

M2

M3

M4

M5

3

3

3

3

3

0

1

1

2

2

1/2

1/2

3/2

3/2

5/2

2

2

4

4

6

Energy levels of the K-, L- and M-shells(n - principal, l- azimuthal quantum numbers;j spin-orbit coupling)


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The binding energy of inner electrons in the atom is of the same order ofmagnitude as the energy of the X-ray photons.

X-rays can interact with the inner shell electrons.

Sub-shell K L1 L2 L3

Binding energy (keV) 8.981 1.102 0.953 0.933

Energy levels in copper


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The interaction of X-rays with atomic electrons

absorption of the photon

photoelectric absorption is the dominant interaction, causes thegeneration of the characteristic X-rays in the sample.

scattering of the photonresponsible for most of the continuum observed in XRFspectra (part of the exciting radiation is scattered by thesample and enters the detector system)


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Photoelectric absorption

a photon is completely absorbed by the atom an (inner shell) electron is ejected.

Part of the photon energy is used to overcome the binding energy of the electron,the rest is transferred to the electron in the form of kinetic energy

After the interaction, the atom (actually ion) is in a highly excited state. A vacancy has been created in one of the inner shells.

The atom will almost immediately return to a more stable electron configuration emission of an Auger electron or a characteristic X-ray photon.

Photoelectric absorption can only occur if EPhoton > Eab !!!

The probability of the emission of characteristic x-ray is calledthefluorescent yield, .


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Thephotoelectric cross section of copperas function of the energy of the interacting photon ph (E)

At high energy the probability of ejecting a electron is rather low

Cu

At 8.98 keV there is an abrupt decrease in the cross section X-rays with lower energy can only interact with the L- and M- electrons.

At E slightly greater than 8.98 keV the cross section is higher !!!

absorptionedges

The ratio of the cross section just above and just below the absorption edgeis called thejump ratio, r.


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Elem. Absorption edge energy (keV) Absorption edge wavelength ()

K L3 M5 K L3 M5

C 6 0.283 43.767

Si 14 1.837 0.098 6.745 127

Ca 20 4.037 0.349 3.070 35.5

Cr 24 5.987 0.574 2.070 21.6

Fe 26 7.109 0.708 1.743 17.5

Ni 28 8.329 0.853 1.488 14.5

Sr 38 16.101 1.940 0.770 6.387

Rh 45 23.217 3.001 0.534 4.130

Ba 56 37.399 5.245 0.780 0.331 2.363 15.89W 74 69.479 10.196 1.814 0.178 1.216 6.83

Pb 82 88.037 13.041 2.502 0.141 0.950 4.955

U 92 115.61 17.160 3.545 0.108 0.722 3.497

Absorption edge energies and wavelengths for some elements


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Elastic and Inelastic Scattering

Scattering causes the photon to change direction.

Elastic or Rayleigh scattering

The energy of the photon is the same before and after scattering Occurs on bound electrons

Forms the basis of X-ray diffraction.

e-K L M

> Compton Scatter

Rayleigh Scatter

'

Inelastic or Compton scattering

The photon loses some of its energy Occurs when X-ray photons interact with weakly bound electrons.

A photon with energyE, inelasticly scattered over an angle will have anenergyE'given by the Compton equation:

)cos1(511

1 -E

+

E=E

E= 20 keV, = 90 E'= 19.25


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X-ray attenuation

X-rays pass through matter some photons will be affected

by photoelectric absorption

by scatteringThe intensityI0 of an X-ray beam passing through a layer of thickness danddensity is reduced to an intensityIaccording to the well-known law ofLambert-Beer:

)exp(0 dII =

The number of photons (the intensity) is reduced but their energy is

unchanged. is called the mass attenuation coefficientand has thedimension of [cm2/g]. The total mass attenuation coefficient is thecontribution from photo-electric absorption, coherent and incoherentscattering

IncCohPhoto ++=


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Log-log plot of the mass attenuation coefficient of aluminium, iron, and leadfor X-rays with energies between 0.1 and 50 keV.

The absorption edge discontinuities due to photoelectric absorption are clearlyvisible.

Low Z materials (Al) attenuate X-rays less than high Z materials (Pb). High energy (hard) X-rays are attenuated less than low energy (soft) X-rays.


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The mass attenuation coefficient of a complex matrix

(a compound, a mixture or an alloy) can be calculated as:

w= ii

n

=i

1

M

i - the mass attenuation coefficient element iw

i- the weight fraction of element i

Radiation Mass attenuation coefficient

in cm2/g of absorberLine keV O Si Fe Pb

O K-L3,2 0.525 23.6 1270 7930 4000 12300

Si K-L3,2 1.74 7.13 1050 360 2490 1970

Fe K-L3,2 6.40 1.94 23.5 124 75.5 426

Ni K-L3,2 7.47 1.66 14.6 78.7 389 286


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Characteristic X-rays emission

After photoelectric absorption the atom is in a highly excited state.

The vacancy will be filled by an electron from a higher shell.

The energy difference between those two states, (vacancy in the K-shell and vacancy in the L3-shell) can be emitted as an X-ray photon.

These X-rays are called "characteristic" because their energy isdifferent for each element, as every element has its own energy level.

The emission governed by quantum mechanical selection rules.

n > 0, l= 1, and j = 0 or 1.

Those give rise to the allowedordiagram lines.Forbiddentransitions have very low intensity.


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K-lines: X-ray lines that originate from a vacancy in the K-shell

L3 K transition

X-ray with an energyof 6.404 keV (1.9360 )(Fe K-L3 or Fe K1)

L2 K transition Fe K-L2or K2 line doublet with very

small energy difference

K-L3,2 or K

M- or N-shell transitions

K lines higher energy, butless intensity

Transition diagram of iron


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L- and M-lines

L-lines result from filling a vacancy in the L-shell.

There are 3 (L1, L2 and L3) sub-shells the L-line spectrum is morecomplex than the K-line spectrum.

L-lines are used to determine elements with an atomic number greater than45 (Rh).

The L3-M5,4 (L) line is the most suitable analytical line. In case of

interference, the L2-M4 (L) line can be used.

M-lines are due to a vacancy in one of the five M sub-cells

Seldom used in XRF.

The M-lines of the heavy elements (Pb) can interfere with K- and L-linesfrom lowerZelements (S).


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Principal X-ray diagram lines, IUPAC, and Siegbahn notation,and their intensity relative to the major line in each sub-shell

Notation Relative

IUPAC Siegbahn intensity

K-lines K-L3

K-L2

K-M3

K-M2

K1

K2

K1K3

100

~50

~17

~8

L3-lines L3-M5

L3-M4

L3-N5,4

L3-M1

L3-N1

L1

L2

L2,15

Ll

L6

100

~10

~25

~5

~1

L2-lines L2-M4

L2-N4

L2-M1

L2-O1

L1

L1

L

L6

100

~20

3

3

L1-lines L1-M3

L1-M2

L1-N3

L1-N2

L3

L4

L3

L2

100

~70

~30

~30

M-lines M5-N7

M5-N6

M4-N6

M1

M2

M

fK

is the K to total K

(K+K) ratio


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Energy in keV of the major characteristic lines of some elements

Elem. K-L3(K1)

K-L2(K2)

K-M3(K1)

K-M2(K3)

L3-M5(L1)

L2-M4(L1)

M5-N5,7(M)

C 6 0.525Si 14 1.740

Ca 20 3.692 3.688 4.013 0.341Cr 24 5.415 5.406 5.947 0.573 0.583Fe 26 6.404 6.391 7.058 0.705 0.719

Ni 28 7.478 7.461 8.265 0.852 0.869Sr 38 14.165 14.098 15.836 15.825 1.807 1.872

Rh 45 20.216 20.074 22.724 22.699 2.697 2.834Ba 56 32.194 31.817 36.378 36.304 4.451 4.828W 74 59.318 57.982 67.244 66.951 8.398 9.672 1.775Pb 82 74.969 72.804 84.936 84.450 10.552 12.614 2.345U 92 98.439 94.665 111.300 110.406 13.615 17.220 3.171


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Fluorescence yield and Auger electron emission

The energy released when an L-electron drops into a K-vacancy can also betransferred to another L- (or M-) electron

The electron receives sufficient energy to leave the atom and is called an Auger

electron.The probability that the vacancy will result in X-ray emission is called the

fluorescence yield, e.g., for the K-shell:

createdsK vacancieofNumber

emittedraysXKofNumberK

=

Kis very small (~0.01) for elementsbelow sodium (Z = 11)

For high Z elements Ktends towardone

XRF is less sensitive for lightelements, many vacancies are created,

but only few characteristic X-rays areemitted.


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Calculation of Mass Attenuation Coefficients:

the Wernisch Algorithm.

The total mass attenuation coefficient

in cm2g-1 can be calculated using the relation:

Ekd

He

ln+

=

E the energy of the x-ray in keV

k a constant for each edgeH a constant for each sub-edge

d a function of the atomic number, Z, of the absorber


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Ekd

He

ln+

=

Depending on the regionbelow the M-edge (D), the L-edge C,

the K-edge (B) or above the K-edge (A)different constants are used


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EnergyRange

k d0 d1 d2 d3 d4

E>EK -2.685 5.955 3.917 10-1 -1.054 10-2 1.520 10-4 -8.508 10-7EL3


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To calculate the edge energies, Wernisch proposed the following equation

32 ZnZtZsrE iiiii +++=

With Ei the energy in keV of a particular edge i

Z the atomic number of the atom

ri,si, ti, ni coefficients for a particular edge i, given in the table

Edge rI si ti nI Zmin Zmax

K-1.30410

-1

-2.63310

-3

9.71810

-3

4.14410

-5 11 63

L1 -4.50610-1

1.56610-2 7.59910-4 1.79210-5 28 83

L2 -6.01810-1

1.96410-2 5.93510-4 1.84310-5 30 83

L3 3.39010-1

-4.93110-2 2.33610-3 1.83610-6 30 83

M1 -8.645 3.97710-1

-5.96310-3 3.62410-5 52 83

M2 -7.499 3.45910-1 -5.25010-3 3.26310-5 55 83M3 -6.280 2.83110

-1-4.11710-3 2.50510-5 55 83

M4 -4.778 2.18410-1

-3.30310-3 2.11510-5 60 83

M5 -2.421 1.17210-1 -1.84510-3 1.39710-5 61 83

See MACWernisch.xls

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